An example of set factory#

The goal of this module is to exemplify the use of set factories. Note that the code is intentionally kept minimal; many things and in particular several iterators could be written in a more efficient way.

See also

set_factories for an introduction to set factories, their specifications, and examples of their use and implementation based on this module.

We describe here a factory used to construct the set \(S\) of couples \((x,y)\) with \(x\) and \(y\) in \(I:=\{0,1,2,3,4\}\), together with the following subsets, where \((a, b)\in S\)

\[ \begin{align}\begin{aligned}S_a := \{(x,y) \in S \mid x = a\},\\S^b := \{(x,y) \in S \mid y = b\},\\S_a^b := \{(x,y) \in S \mid x = a, y = b\}.\end{aligned}\end{align} \]

class sage.structure.set_factories_example.AllPairs(policy)#

Bases: ParentWithSetFactory, DisjointUnionEnumeratedSets

This parent shows how one can use set factories together with DisjointUnionEnumeratedSets.

It is constructed as the disjoint union (DisjointUnionEnumeratedSets) of Pairs_Y parents:

\[S := \bigcup_{i = 0,1,..., 4} S^y\]

Warning

When writing a parent P as a disjoint union of a family of parents P_i, the parents P_i must be constructed as facade parents for P. As a consequence, it should be passed P.facade_policy() as policy argument. See the source code of pairs_y() for an example.

check_element(el, check)#

pairs_y(letter)#

Construct the parent for the disjoint union

Construct a parent in Pairs_Y as a facade parent for self.

This is an internal function which should be hidden from the user (typically under the name _pairs_y. We put it here for documentation.

class sage.structure.set_factories_example.PairsX_(x, policy)#

Bases: ParentWithSetFactory, UniqueRepresentation

The set of pairs \((x, 0), (x, 1), ..., (x, 4)\).

an_element()#

check_element(el, check)#

class sage.structure.set_factories_example.Pairs_Y(y, policy)#

Bases: ParentWithSetFactory, DisjointUnionEnumeratedSets

The set of pairs \((0, y), (1, y), ..., (4, y)\).

It is constructed as the disjoint union (DisjointUnionEnumeratedSets) of SingletonPair parents:

\[S^y := \bigcup_{i = 0,1,..., 4} S_i^y\]

See also

AllPairs for how to properly construct DisjointUnionEnumeratedSets using ParentWithSetFactory.

an_element()#

check_element(el, check)#

single_pair(letter)#

Construct the singleton pair parent

Construct a singleton pair for (self.y, letter) as a facade parent for self.

See also

AllPairs for how to properly construct DisjointUnionEnumeratedSets using ParentWithSetFactory.

class sage.structure.set_factories_example.SingletonPair(x, y, policy)#

Bases: ParentWithSetFactory, UniqueRepresentation

check_element(el, check)#

class sage.structure.set_factories_example.XYPair(parent, value, check=True)#

Bases: ElementWrapper

A class for Elements \((x,y)\) with \(x\) and \(y\) in \(\{0,1,2,3,4\}\).

EXAMPLES:

sage: from sage.structure.set_factories_example import XYPair
sage: p = XYPair(Parent(), (0,1)); p
(0, 1)
sage: p = XYPair(Parent(), (0,8))
Traceback (most recent call last):
...
ValueError: numbers must be in range(5)

sage.structure.set_factories_example.XYPairs(x=None, y=None, policy=None)#

Construct the subset from constraints.

Consider the set \(S\) of couples \((x,y)\) with \(x\) and \(y\) in \(I:=\{0,1,2,3,4\}\). Returns the subsets of element of \(S\) satisfying some constraints.

INPUT:

x=a – where a is an integer (default to None).
y=b – where b is an integer (default to None).
policy – the policy passed to the created set.

See also

set_factories.SetFactoryPolicy

EXAMPLES:

Let us first create the set factory:

sage: from sage.structure.set_factories_example import XYPairsFactory
sage: XYPairs = XYPairsFactory()

One can then use the set factory to construct a set:

sage: P = XYPairs(); P.list()
[(0, 0), (1, 0), (2, 0), (3, 0), (4, 0), (0, 1), (1, 1), (2, 1), (3, 1), (4, 1), (0, 2), (1, 2), (2, 2), (3, 2), (4, 2), (0, 3), (1, 3), (2, 3), (3, 3), (4, 3), (0, 4), (1, 4), (2, 4), (3, 4), (4, 4)]

Note

This function is actually the __call__ method of XYPairsFactory.

class sage.structure.set_factories_example.XYPairsFactory#

Bases: SetFactory

An example of set factory, for sets of pairs of integers.

See also

set_factories for an introduction to set factories.

add_constraints(cons, args_opts)#

Add constraints to the set cons as per SetFactory.add_constraints.

This is a crude implementation for the sake of the demonstration which should not be taken as an example.

EXAMPLES:

sage: from sage.structure.set_factories_example import XYPairs
sage: XYPairs.add_constraints((3,None), ((2,), {}))
Traceback (most recent call last):
...
ValueError: Duplicate value for constraints 'x': was 3 now 2
sage: XYPairs.add_constraints((), ((2,), {}))
(2, None)
sage: XYPairs.add_constraints((), ((2,), {'y':3}))
(2, 3)